The Foundations of Geometry
The Foundations of Geometry
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In our eReader you can find the full English version of the book. Read The Foundations of Geometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Foundations of Geometry
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If not AC intersects the r. F. In a single point Q, and the s. 1. PQ is in both p. And r. F. And they cannot intersect in any point outside PQ (HI. 2).
VI. Two parallel r. F s. Cannot intersect; and any two which are not parallel intersect in a p.
For if ABCD, EFGH be two r. F s. Which are not parallel, and A be any point in the first which is not in the second, then EFGH is not parallel to all of AB, AC, AD. Therefore it intersects at least one of them 96 PART III.
in a single point, P (III. 4...). And EFGH is not parallel to either of the p s. ABC, ABD. Therefore it intersects each of them in a s. 1. PQ, PR (III. 5). Therefore also the p. PQR is in both r. F s. And they cannot intersect in any point outside this p. (III. 2).
VII. Any two p s. Extending in four i. D s. Intersect in a single point.
For if A BC, DEF be two p s. Which extend in four i. D s. , and if A be any point in the first which is not in the second, then the direction AD is not independent of the four i. D s. AB, AC, DE, DF (P).
What to read after The Foundations of Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Edward T Edward Travers Dixon to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
If not AC intersects the r. F. In a single point Q, and the s. 1. PQ is in both p. And r. F. And they cannot intersect in any point outside PQ (HI. 2).
VI. Two parallel r. F s. Cannot intersect; and any two which are not parallel intersect in a p.
For if ABCD, EFGH be two r. F s. Which are not parallel, and A be any point in the first which is not in the second, then EFGH is not parallel to all of AB, AC, AD. Therefore it intersects at least one of them 96 PART III.
in a single point, P (III. 4...). And EFGH is not parallel to either of the p s. ABC, ABD. Therefore it intersects each of them in a s. 1. PQ, PR (III. 5). Therefore also the p. PQR is in both r. F s. And they cannot intersect in any point outside this p. (III. 2).
VII. Any two p s. Extending in four i. D s. Intersect in a single point.
For if A BC, DEF be two p s. Which extend in four i. D s. , and if A be any point in the first which is not in the second, then the direction AD is not independent of the four i. D s. AB, AC, DE, DF (P).
What to read after The Foundations of Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Edward T Edward Travers Dixon to read onlineMoreLess
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